Since you do have both audio and video briefly,
this indicates that the more complex section of your set is working.
The assembly that most affects these two equally
is the power supply and this is a common failure in all too many of more
recently built TVs.
The supply is normally built on a separate board
since these are often out-sourced by set manufacturers.
Unplug your set overnight to allow potentially
hazardous voltages to discharge, remove the back panel of the set so you can
see the guts.
Look for a smaller board with larger parts on
it; some cylindrical (capacitors), others block-like and relatively large
(chokes and transformers).
You should also see a relationship between the
board and the incoming AC.
Check the board for a label or if not present, a
stamped-on number.
Call the manufacturer's service center with your
TV model number and the number found on that board and inquire about
repair/replacement costs; if both are offered, they won't be that much
different.
If you must buy a new board, don't dispose of
the failed one as there are smaller companies that can repair it for less than
the mfr. and then keep it as a spare as this problem will likely arise again.
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